Neural Descriptors: Self-Supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches

• URL: http://arxiv.org/abs/2503.03907v1
• Date: Wed, 05 Mar 2025 21:15:14 GMT
• Title: Neural Descriptors: Self-Supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches
• Authors: Gal Yona, Roy Velich, Ron Kimmel, Ehud Rivlin,
• Abstract summary: We present a self-supervised learning approach for extracting geometric features from 3D surfaces.<n>Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features.
• Score: 11.450257794341052
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling patterns, and topological noise. While differential geometry offers a promising alternative through its theory of differential invariants, which are theoretically guaranteed to be robust shape descriptors, the computation of these invariants on discrete meshes often leads to unstable numerical approximations, limiting their practical utility. We present a self-supervised learning approach for extracting geometric features from 3D surfaces. Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features. By integrating our features into existing shape correspondence frameworks, we demonstrate improved performance on standard benchmarks including FAUST, SCAPE, TOPKIDS, and SHREC'16, showing particular robustness to topological noise and partial shapes.

Related papers

• Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations [0.0]
  We introduce enf2enf, an encoder--decoder methodology for predicting steady-state Partial Differential Equations. Our method supports real time inference and zero-shot super-resolution, enabling efficient training on low-resolution meshes.
  arXiv  Detail & Related papers  (2025-04-24T08:30:32Z)
• Differentiable Topology Estimating from Curvatures for 3D Shapes [5.122262236258208]
  This paper introduces a novel, differentiable algorithm tailored to accurately estimate the global topology of 3D shapes.<n>It ensures high accuracy, efficiency, and instant computation with GPU compatibility.<n> Experimental results demonstrate the method's superior performance across various datasets.
  arXiv  Detail & Related papers  (2024-11-28T17:14:35Z)
• Geometry Distributions [51.4061133324376]
  We propose a novel geometric data representation that models geometry as distributions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity.
  arXiv  Detail & Related papers  (2024-11-25T04:06:48Z)
• Irregular Tensor Low-Rank Representation for Hyperspectral Image Representation [71.69331824668954]
  Spectral variations pose a common challenge in analyzing hyperspectral images (HSI)<n>Low-rank tensor representation has emerged as a robust strategy, leveraging inherent correlations within HSI data.<n>We propose a novel model for irregular tensor lowrank representation tailored to efficiently model irregular 3D cubes.
  arXiv  Detail & Related papers  (2024-10-24T02:56:22Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• GSMFlow: Generation Shifts Mitigating Flow for Generalized Zero-Shot Learning [55.79997930181418]
  Generalized Zero-Shot Learning aims to recognize images from both the seen and unseen classes by transferring semantic knowledge from seen to unseen classes. It is a promising solution to take the advantage of generative models to hallucinate realistic unseen samples based on the knowledge learned from the seen classes. We propose a novel flow-based generative framework that consists of multiple conditional affine coupling layers for learning unseen data generation.
  arXiv  Detail & Related papers  (2022-07-05T04:04:37Z)
• Exemplar-bsaed Pattern Synthesis with Implicit Periodic Field Network [21.432274505770394]
  We propose an exemplar-based visual pattern synthesis framework that aims to model inner statistics of visual patterns and generate new, versatile patterns. An implicit network based on generative adversarial network (GAN) and periodic encoding, thus calling our network the Implicit Periodic Network (IPFN)
  arXiv  Detail & Related papers  (2022-04-04T17:36:16Z)
• Feature Engineering with Regularity Structures [4.082216579462797]
  We investigate the use of models from the theory of regularity structures as features in machine learning tasks. We provide a flexible definition of a model feature vector associated to a space-time signal, along with two algorithms which illustrate ways in which these features can be combined with linear regression. We apply these algorithms in several numerical experiments designed to learn solutions to PDEs with a given forcing and boundary data.
  arXiv  Detail & Related papers  (2021-08-12T17:53:47Z)
• Primal-Dual Mesh Convolutional Neural Networks [62.165239866312334]
  We propose a primal-dual framework drawn from the graph-neural-network literature to triangle meshes. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them. We provide theoretical insights of our approach using tools from the mesh-simplification literature.
  arXiv  Detail & Related papers  (2020-10-23T14:49:02Z)
• Instant recovery of shape from spectrum via latent space connections [33.83258865005668]
  We introduce the first learning-based method for recovering shapes from Laplacian spectra. Given an auto-encoder, our model takes the form of a cycle-consistent module to map latent vectors to sequences of eigenvalues. Our data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost.
  arXiv  Detail & Related papers  (2020-03-14T00:48:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.